2010 Fiscal Year Final Research Report
Discrete mathematics for coding theory and cryptography
| Project/Area Number |
20740051
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ochanomizu University |
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Principal Investigator |
HAGITA Mariko Ochanomizu University, 大学院・人間文化創成科学研究科, 准教授 (70338218)
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| Project Period (FY) |
2008 – 2010
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| Keywords | グラフ彩色 / ド・ブライン / 暗号 / 誤り訂正符号 / 離散数学 |
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| Research Abstract |
We define an (N,k,d) error-correcting sequence over GF(q) as a periodic sequence a_0,a_1,a_2,... of elements in GF(q) with period N, such that its sub k-tuples (a_i, a_{i+1}, ..., a_{i+k-1}) are all distinct for i=0,1,...N-1, and they form an error-correcting code with minimum distance d.
Admitting a moderate conjecture on the existence of primitive polynomials whose coeffients constitute a De Bruijn sequence or a Projective De Bruijn sequence, we prove the existence of a binary (2^{2^m-m-2}-1,2^m-2,3) error-correcting sequence and (q^{\frac{q^m-1}{q-1}-m}-1,\frac{q^m-1}{q-1},3) error-correcting sequence over GF(q).
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Research Products
(17 results)
